I don't really have time to respond to your comments right now, but I did want to make one tangential remark. Mathematics is absolute, but it's only valid wi

I don't really have time to respond to your comments right now, but I did want to make one tangential remark. Mathematics is absolute, but it's only valid within the abstract context of that branch of mathematics. Mathematics itself went through a paradigm shift in the early 20th century, known as the "foundational crisis". At the time, mathematicians began running into paradoxes which existing theories could not properly address, including Russel's Paradox. In response, mathematicians developed a set of formal axioms (nowadays most people use ZFC, although sometimes Von Neumann–Bernays–Gödel and other variations are used) which produce a mathematical foundation that is consistent (i.e. free of paradoxes/contradictions). However, as Gödel's Incompleteness Theorems demonstrated, there is no set of foundational axioms which are both consistent (free of contradictions) and complete (all mathematical truths can be deduced by such a system). So, while it is true that mathematical proofs are formally valid deductions from a set of axioms, it is worth recognizing that the relationship between mathematics and truth are somewhat more complex than they seem. As it stands, there are an infinite number of mathematical statements that cannot be derived by an axiomatic system. Some philosophers have even sought to identify 'quasi-empiricism' in mathematical thought [1]. And if you find that interesting, you'll love James Conant's paper on Logically Alien Thought [2]. [1] http://en.wikipedia.org/wiki/Quasi-empiricism_in_mathematics http://en.wikipedia.org/wiki/Quasi-empiricism_in_mathematics [2] http://philosophy.uchicago.edu/faculty/files/conant/Search%20for%20Logically%20Alien%20Thought%20-%20clean%20searchable%20copy.pdf http://philosophy.uchicago.edu/faculty/files/conant/Search%2...